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If 3|3 – x| = 7, what is the product of all the possible va

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nave
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If 3|3 – x| = 7, what is the product of all the possible va [#permalink] New post  28 Mar 2013, 21:09
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If 3|3 – x| = 7, what is the product of all the possible values of x?

A. 1/9
B. 1/3
C. 2/3
D. 16/9
E. 32/9
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Re: If 3|3 – x| = 7, what is the product of all the possible va [#permalink] New post  29 Mar 2013, 00:29
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\(3|3 - x| = 7\)
case \(3-x>0\)
\(3(3-x)=7\)
\(9-3x=7, x=\frac{2}{3}\)
case \(3-x<0\)
\(3(-3+x)=7\)
\(-9+3x=7, x= 16/3\)

\(\frac{2}{3}*\frac{16}{3}=\frac{32}{9}\)
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Re: If 3|3 – x| = 7, what is the product of all the possible va [#permalink] New post  28 Mar 2013, 21:40
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nave81 wrote:
If 3|3 – x| = 7, what is the product of all the possible values of x?

A. 1/9
B. 1/3
C. 2/3
D. 16/9
E. 32/9


3|3-x| = 7 can be rewritten as: \(|3-x| = \frac{7}{3}\)

So

\(|\frac{9}{3} - x| = \frac{7}{3}\)

x has two possible solutions \(\frac{2}{3}\) and \(\frac{16}{3}\) that satisfy the equation

\(\frac{2}{3}*\frac{16}{3} = \frac{32}{9}\)

Answer is E
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Re: If 3|3 – x| = 7, what is the product of all the possible va [#permalink] New post  01 Apr 2013, 08:00
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nave81 wrote:
If 3|3 – x| = 7, what is the product of all the possible values of x?

A. 1/9
B. 1/3
C. 2/3
D. 16/9
E. 32/9


3|3 – x| = 7 So, |3 – x| = 7/3 or (3-x) = +7/3 or -7/3
Solving we get x = 2/3 or 16/3
product = \(2/3 * 16/3 = 32/9\)
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Re: If 3|3 – x| = 7, what is the product of all the possible va [#permalink] New post  10 Jul 2013, 10:38
If 3|3 – x| = 7, what is the product of all the possible values of x?

x≥3, x<3

x≥3:
3|3 – x| = 7
3 -(3-x) = 7
3 (-3+x) = 7
-9 + 3x = 7
3x = 16
x=16/3 Valid

x<3
3(3-x) = 7
9-3x = 7
-3x=-2
x=2/3

(16/3)*(2/3) = 32/9

(E)
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Re: If 3|3 – x| = 7, what is the product of all the possible va [#permalink] New post  09 Mar 2016, 05:40
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I don't agree with E. 16/3, when substituted in the original equation doesn't satisfy it. you would get |-9/3| = 7/3 which is not legit. So we should discard 16/3 as a solution of the equation. That leaves us with 2/3 which is option C

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Dheeraj Rekula
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Re: If 3|3 – x| = 7, what is the product of all the possible va [#permalink] New post  09 Mar 2016, 06:35
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nave wrote:
If 3|3 – x| = 7, what is the product of all the possible values of x?

A. 1/9
B. 1/3
C. 2/3
D. 16/9
E. 32/9


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If 3|3 – x| = 7, what is the product of all the possible va [#permalink] New post  09 Mar 2016, 06:38
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Caesar_1987 wrote:
If 3|3 – x| = 7, what is the product of all the possible values of x?

A. 1/9
B. 1/3
C. 2/3
D. 16/9
E. 32/9

I don't agree with E. 16/3, when substituted in the original equation doesn't satisfy it. you would get|-9/3| = 7/3 which is not legit. So we should discard 16/3 as a solution of the equation. That leaves us with 2/3 which is option C

Best Regards
Dheeraj Rekula


16/3 does satisfy the equation:
3|3 – 16/3| = 7;
3*7/3 = 7.

Hope it's clear.
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Re: If 3|3 – x| = 7, what is the product of all the possible va [#permalink] New post  13 Mar 2017, 01:19
3|3-x| = 7 can be rewritten as: |3−x|=7/3
so we have
1. 3-x =7/3
x=2/3

2. 3-x=-7/3
x=16/3

so product will be
32/9
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Re: If 3|3 – x| = 7, what is the product of all the possible va [#permalink] New post  10 Mar 2018, 10:51
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nave wrote:
If 3|3 – x| = 7, what is the product of all the possible values of x?

A. 1/9
B. 1/3
C. 2/3
D. 16/9
E. 32/9



Given : 3|3 – x| = 7

3 – x = 7/3 or 3 – x = -7/3

x = 2/3 or 16/3

Product of all the possible values of x = 2/3 * 16*3 = 32/9

(E)
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Re: If 3|3 – x| = 7, what is the product of all the possible va [#permalink] New post  12 Mar 2019, 07:13
the equation leads to two values of x
2/3 , 16/3
their product equals to 32/9 i.e. E
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Re: If 3|3 x| = 7, what is the product of all the possible va [#permalink] New post  28 Jun 2023, 21:54
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